These three parts contain the proceedings of the AMS Summer Institute on Differential Geometry, held at the University California, Los Angeles in July 1990. This was the largest AMS Summer Institute ever, reflecting the wide-ranging and intense research activity in the subject. The parts contain many extensive survey articles presenting perspectives on relatively broad topics; these articles would be accessible to advanced graduate students. In addition, the authors of the research articles were encouraged to survey the relevant literature. The three parts together offer the deepest and most comprehensive survey of recent research in differential geometry available today.